The following line passes through point $(-6, -5)$ : $y = \dfrac{9}{4} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-6, -5)$ into the equation gives: $-5 = \dfrac{9}{4} \cdot -6 + b$ $-5 = -\dfrac{27}{2} + b$ $b = -5 + \dfrac{27}{2}$ $b = \dfrac{17}{2}$ Plugging in $\dfrac{17}{2}$ for $b$, we get $y = \dfrac{9}{4} x + \dfrac{17}{2}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ $(-6, -5)$